When I created the harmonic school of Bimodalism in the late 1950s, I
thought it should have occurred as a musical discipline before the advent of
atonality. But, as we know, it did not.

Perhaps, Bimodalism should have been a middle road between the followers
and abandoners of tonality. But this did not happen either.

In retrospect, we can observe how the development of harmony correlates
chronologically to the phenomenon of the harmonic series: As each period in
music history came about, harmonic intervals of sounds, corresponding in
order and pitch to those of the series, gradually integrated a chordal
column of superimposed thirds, a column whose capital was crowned with the
thirteenth chord.

Harmonic evolution, based on the phenomenon of the harmonic series, may
thus be seen as teleological in nature: Sound carried within itself the
harmonic components of the chord, to be revealed as representatives of each
period throughout the history of music.

But regardless of whether this teleological conjecture is confirmable,
the fact is composers did progressively superimpose the seven different
sounds carried in the harmonic series until they attained the culmination of
tertian harmony.

This prompted me to ask, Why then did they not also superimpose the major
and minor modes in a triad, before the dissolution of tonality? Would this
not have been the culmination of tonality?

Perhaps, composers have been too enthusiastic to follow the orientation
of other contemporary schools (such as the Second Vienna School),
overlooking the possibility of modal unity that Bimodalism proposes.

In this sense, by composing in bimodal harmony, I believe I have not only
filled a hitherto unnoticed gap in music history, but have contributed as
well in renewing the development of harmony from the point where late
Impressionism left it.

In this era, where serialist and polytonal decadence force us to invent
extramusical avant-garde procedures, or lead us to excavate the remote
past—as the minimalists have done—in search of magical formulas that might
aerate the blood of our contemporary music, the chance to return to the
realm of harmony presents its most novel and piquant option in Bimodalism.

To return is not always to retreat, but sometimes to resume.

The essence of the harmonic discipline of Bimodalism lies in the
simultaneous blending of major and minor modes in triads with the same
fundamental root.

This blend—the begetter of a new ethos in harmony—is applied generally
throughout an entire musical work, from beginning to end; or in sections
where the musical thought lasts a significant duration of time; or in a
symbiotic form, sharing roles with other existing chordal entities:
symbiotic Bimodalism.

(N.B. Any attachment to a bimodal chord nullifies its harmonic effect
[ethos]: The
polychord, for instance, although it consists strictly of bimodal chords,
actually loses this Bimodal harmonic effect because of the chordal juxtaposition
of notes extending beyond the triad.
Therefore, any use of polychords is discarded in Bimodalism.)

When we listen to music in bimodal harmony, we hear something reminiscent
of the old tonality.

There is a reason for this: Bimodalism forges the two modes that
characterize western music since the seventeenth century, in order to form a
single chord.

It is precisely the bimodal chord. (Although the bimodal chord does in
fact consist of four sounds [such as C-Eb-E-G], I will refer to it as a
triad, in keeping with the lexicon of harmony).

By joining major and minor triads (and only these triads) of the same
root on each degree of the chromatic scale, we obtain 12 bimodal chords of
four notes with their three corresponding inversions—a total of 48 chords.

In turn, these 48 bimodal chords—as each has 44 possibilities of chordal
progressions within the chromatic scale—yield a total of 2112 chordal
progressions for the entire harmonic system, whose chordal progressions bear
a close tonal interrelationship, given the chordal equality that Bimodalism
establishes along the chromatic scale.

Consequently, both remote tonalities and modulation
concepts are senseless in Bimodalism, as it is intrinsically a chain of 12
equivalent and harmonically linked chords, forming, in fact, a true
unitonality—in other words, a Bimodal chord over each degree of the
chromatic scale.

N.B. Although the appearance of certain harmonic entities throughout
contemporary musical history (such as whole tone chords, fourth or fifth
chords, the mystical chord, tone clusters, and others) have made an
impression on our ears, composers have only been able to use these harmonic
entities as accessories to an eclectic compositional style (Puccini), or as
the harmonic emblem of a paradigmatic work (Scriabin), because these
harmonic entities cannot generate a rich musical literature on their own
within the domain of tonality, such as was the case during the heyday of
tertian harmony.

Rudiments and Table of Bimodal Chords

FIG. 1. The example at right shows two notations of the bimodal chord in
its closest position: (a) as it should be written currently; and (b) as it
would appear if we were to use this accidental sign of my own creation. I
propose such a sign for altered and unaltered notes of equal name and
placement that are played simultaneously—in the case of the bimodal chord,
only its third. Similarly, I propose that the third degree of the diatonic
scale be termed as modal, despite the mediant (a merely ordinal term). If
the first and fifth degrees of the scale are denominated by their tonal
function, its third degree, likewise, should then be denominated by its
modal function, since it—and only it—determines the mode in music. Thus, the
first, third and fifth degrees of the scale could be denominated, tonic, modal, and dominant, respectively.

FIG. 2. The example
at left illustrates Bimodal chords on the 12 degrees of
the chromatic scale in enharmonic notation. Notice how each chord
displays the double-letter symbol representing the fusion of both major and
minor modes: Cc, Cc#, Dd, and so forth. They are, however, to be referred to
solely by their root and (mixed) modality: Bimodal C, Bimodal C#, and
Bimodal D, respectively. And in the Guidonian nomenclature: Bimodal
Do,
Bimodal Do#, Bimodal Re, and so forth. (Where you see the asterisk in the
illustration at left, note the following: To avoid any confusion, I employ the
letters B and H as symbols for the B flat and B natural notes, respectively,
following the usage in German nomenclature. Consequently, the bimodal chord
over B flat is written as Bb, and the bimodal chord over B as Hh.)

FIG. 3. The example below illustrates first, second, and
third inversions of the bimodal chord—close and open positions,
respectively. All three inversions, including the defective ones, are
beautiful and well balanced. The first two inversions (chords of the sixth,
open or close),
however, are more characteristic of Bimodalism in their harmonic soundscape
(the Bimodal ethos). I have therefore used them abundantly in my own
bimodal scores, practicing, in fact, a kind of bimodalized sixth-chord style
("fauxbourdon").

N.B. Where you see the asterisk in FIG. 3 above (*), please note that in
Bimodalism, the ever-present double third degree alone defines unmistakably
the identity of a chord. Therefore, you can omit the fifth—and even the
first!—degree of a chord without losing or confusing the harmonic identity
of the same chord. This means you can easily tell if the omitted degree is
the first or the fifth, once you find the the double third of the chord. I refer to this type of chord as a
"minus-one chord" (my own coinage).

FIG. 4. The illustration below shows that in Bimodalism the 12
fundamental chords—each with three corresponding inversions—yield a total of
48 bimodal chords. These 48 chords, when multiplied by the 44 possibilities
of chordal progressions that each may have, yield a total of 2112 chordal
progressions for the entire system.

Bimodalism does not ignore the dynamic law of tension and relaxation that
rules tonality, as do both serial music and polytonality.

Bimodalism, however, does not apply this law through exclusive scalar
degrees, depending on a gravitational center or tonic, as does tonality.

Bimodalism, barring the influence of tonal rules and its metric
restrictions, applies this law to a very free melodic wave that reveals its
proper points of tension and relaxation on any bimodalized chordal degree of
the chromatic scale.

In other words, bimodal tonality allows all sorts of prerogatives in the
syntax of musical discourse.

Nonetheless, although Bimodalism has expanded the harmonic
radius of tonality to its limits, this system can freely resort to the most
common chordal progressions of traditional harmony— by way of
Bimodalizing its triads. (Of course, you could also include nonharmonic
tones in bimodal harmonizations).

In doing so, we experience these chordal progressions harmonically
attired in the bimodal style.

Although Bimodalism is generally applied to work on the degrees of the
chromatic scale, this system can also be applied to any known or invented
scale. In effect, you can then form bimodal chords over the degrees of any such scale
to accompany a given melody by following the guidelines of a homophonic style.

While we are on the subject of invented scales, I would like to propose a
scale that I have dubbed the overtone scale (C-D-E-F#-G-A-Bb-B) because it
encompasses the eight distinct sounds of the harmonic series in an octave.

With this scale, we could stack all eight sounds thereby creating the
overtone chord. This chord contains a harmonic spectrum consisting of waves
that interfere with one another, resulting in a sound that is reminiscent of
the dominant seventh chord, but with a dense and quasi-electronic aural
quality.

I liken the overtone scale and overtone chord to gems whose facets
consist of the components of the harmonic series and that now shine with equal
relief and radiance.

We can think of the overtone scale and chord as the legacy of a long
history that began with Pythagoras and that culminated with the birth of the
founding father of harmony, what we call the natural chord.

Although Bimodalism can resort to other chordal entities with which it
can share harmonic roles, I advise against alternating bimodal chords with
those of tertian harmony beyond the perfect triad.

Neutral fourth chords can also play a compatible role
owing to their tonal neutrality.

There is, however, a specific chord that can share the best harmonic role
with the bimodal chord in a symbiotic relationship: the major chord with an
appoggiatura without resolution.

This non-invertible chord always has its appoggiatura of second minor or
major in the bass, and it can be stored in any of its close or open melodic
positions of root, third, or fifth. (The third position, open or close, is
the best balanced of the three.)

Although
this chord is not bimodal, it has two possibilities to become a bimodal
chord: (1) Its appoggiatura can either be resolved in a bimodal chord, or
(2) its
three upper voices (the major triad) can serve as a triple appoggiatura
resolved in another bimodal chord in a descending movement.

The major chord with an appoggiatura without resolution in the bass may
owe its spatial sound identity to a phenomenon of mere acoustic illusion: We
perceive a sensation of dimensional growth in this chord because the root of
the chord is elevated only in the bass while the upper major triad is
unchanged. (The open triad position intensifies this effect.)

This illusory acoustic phenomenon acts as a sort of harmonic lever, lifting the major triad
pillar onto a higher plane without muddling its sound identity as a major
triad. Because its root is transposed to the supertonic degree, this chord
could easily be dubbed the Paratonal Major Chord (or Paratonal Chord,
for short); and so, by virtue of symmetric paratonality, the first degree of
the triad (in the bass) climbs onto the second degree and assumes its
permanent role as the new root of the chord from that position.

Moreover, contemporary audiences can easily withstand a passage
consisting solely of Paratonal Major Chords, owing to the close relationship
of this chord with its originator, the major chord. (This is yet another
harmonic déjà vu brought about by Bimodalism.)

FIG. 5. The example below illustrates: (1) The major chord with an
appoggiatura without resolution; (2) the major chord with an appoggiatura
resolved in a bimodal chord; and (3) the major chord with an appoggiatura,
whose three upper voices are used as a triple appoggiatura resolved in
another bimodal chord. (N.B. It is a theoretical inconsistency to denominate
the major chord with an appoggiatura without resolution in the bass as an
"eleventh" chord [a common misconception in pop music]: A tertian chord, which is what an eleventh chord really
is, must be integrated by its generic third degree [the modal] so that its
modality may be determined. There are eleventh chords, both major and minor, but if they
lack their corresponding third degree, it is impossible to determine which
mode they belong to.)

For instance, a minor eleventh chord could be:
C-Eb-G-Bb-D-F [11]; whereas, the major, raising its third, seventh, and
eleventh by one halftone could be : C-E-G-B-D-F# [+11]. And the augmented
eleventh chord, whose prominent effect makes it the ace of the group, could
be: C-E-G-Bb-D-F# [7+11].)

As we can conclude from this discussion, an aesthetic aim of Bimodalism
is to evoke tonality in its most remarkable of fundaments.

Bimodalism dresses the chordal progressions of traditional harmony in the
attire of the bimodal harmonic style, allowing us to use any known or
invented scale as a fertile ground where bimodal harmony can also flourish.

Bimodalism also allows us to resort to other chordal entities to share
harmonic roles that are symbiotic with the bimodal chord.

Taking into account that Bimodalism can be freely applied with no
previous compositional scheme, we see how the bimodal chord can also
generate textures of an extratonal nature, applying a procedure of musical
writing of my own design, whose aural results I coined "symmetrical
paratonalism." (This is not to be confused with the single-term "paratonality"
as employed by John Vincent in his book, The Diatonic Modes in Modern Music,
published in 1974.)

My term defines the simultaneity of a voice with its doubling
systematically transposed to another tonality by only a major or minor
third, or by only a major or minor sixth.

But symmetrical paratonalism should not be judged as a procedure of
bitonality, when this sort of twin paratonalism works within a homophonic
texture of bimodal harmony, without any adherence to extratonal elements
that may attenuate or nullify its pure effect, such as may sometimes occur
in bitonality. (Cf.: Milhaud’s "Le boeuf sur le toit" [Part H, from measure
188 through 202]).

In applying symmetrical paratonalism, music originally composed for two
voices (e.g. melody and its counterpart, or melodies in counterpoint) will
be magnified and tonally enriched: Transpositions and doublings of every
voice departing from every note of a bimodal chord obtain this effect.

Thus, the melody and its transposed doubling might depart from two notes
of the bimodal chord, a third or sixth apart, whereas the transposed
counterpart with its retransposed doubling depart from the two remaining
notes of this chord.

(Restriction: A symmetrical paratonal combination that originates
harmonic intervals of diminished or augmented octaves, in the doubling of a
same voice, must be avoided: It destroys the aural effect and ethos of
Bimodalism).

FIG. 6A. This illustration shows how symmetrical paratonal writing
magnifies and bimodalizes a tonal passage originally written for two voices.

FIG. 6B. This is a strict eight-measure canon derived from the former
theme appearing in Fig. 6A. If certain notes, notwithstanding, from
symmetric
paratonal writing were incompatible with the Bimodal ethos, you could change
them in favor of Bimodalism.

In addition, a simpler variant of symmetrical paratonalism can generate a
full bimodal harmony when scales, arpeggios, or broken chords of identical
patterns charmingly transfigure their old look, as they depart from each
voice of a bimodal chord in parallel motion.

FIG. 7. This illustration below shows how a scalar symmetrical
paratonalism can be made from each note of a bimodal chord. In this example,
the inverted Cc chord originates and juxtaposes the Eb, G, C, and E scales. The same
procedure can be used on arpeggios, broken chords, and so forth.

Such a magnification of the musical writing for two voices, forming
symmetrical paratonal duos with harmonic intervals of thirds and sixths
only, places these traditional consonancies in the new aural dimension of
Bimodalism.

From this dimension, they evoke a singular flavor of Mediterranean idiom
that is as copious as it is core to our western music.

The terms Bimodalism and bitonality are by no means interchangeable.
Bitonality (or polytonality) is a contrapuntal style of writing music, where
each of two or more diatonic melodies is written in a different tonality, so
that all may sound simultaneously.

But because each melody shares equal prominence, creating a dissonant
field of voices in collision, the ear cannot differentiate the tonality of
each melody nor can it find the resulting tonality from a summation of
combined tonalities. This is evidence that polytonality is, in fact, atonal.

The reality is that the concurrent function of various
tonalities that polytonality prescribes betrays the aesthetic idea behind
its conception, and loses the defining ethos that would otherwise
differentiate it from atonality.

Only when two tonalities are superimposed a tritone apart (such as C
to
F#), and the counterpoint between them is carefully treated, can our ears
sense a certain feeling of tonality, derived from that bipolar interaction.
(Bear in mind that between the C and F# tonalities there are only two notes
in common: B and E# [F].)

Hence, polytonal composers have so often used this bitonal formula, above all, in
the orchestra, where different plans of timbres and nuances favor this
stratiform style of writing.

In contrast, the superimposition of major and minor triads
of a same tonality (such as C and Cm) is not proper of bitonality; if this
were to occur, it would be done following the technique of bitonality, where
each of two autonomous melodies would be written in a different mode of the
same tonality, forming a contrapuntal plot exempt from harmonic ties; in
other words, a counterpoint where every occurrence of Bimodal harmony would
always be welcome, and not preceptual, as it is in Bimodalism.

Consequently, if two melodies were written in separate
modes of a tonality with no harmonic coupling they would sound discordant and turbid, as in any other bitonal combination.
(A rich harmonization, notwithstanding, of Bimodal chords over a basso
ostinato of a specific tonality could well emulate the optimal effect of the
well-known Boléro.)

Indeed, when bitonality does superimpose major and minor tonalities, it
always does so by superimposing remote tonalities of different roots (such
as C and Ebm), whose tonal disparity in the scalar degrees may produce the most contrasting display of aural plans, which is
the primary objective of bitonality.

As we can see, case by case, bitonality differs from
Bimodalism as much in theory as in practice.

Bimodalism, in contrast, is the new harmonic style of homophony.
In it, there is but one melody, harmonized with Bimodal triads.

Notwithstanding, Bimodalism could lend itself to counterpoint, provided
one were to keep the polyphonic texture within a bimodal harmonic framework,
where a certain sensation of tonality is always present.

This sensation of tonality, owing to the fusion of two
modes into one, may
incline one to think of Bimodalism as the maker of a sort of neotonality,
but never as an offspring of bitonality—as some might mistakenly consider
it.

Bimodalism, moreover, bears no resemblance to the twelve-tone technique
in its use of the chromatic scale. The differences between Bimodalism and
the twelve-tone technique are fundamental:

The twelve-tone technique—envisioned by Schoenberg as well as by Hauer—organizes the 12 degrees of the chromatic
scale to nullify tonality. Bimodalism, in contrast, builds a new chord
system on the same degrees, serving to restore and harmonically enrich tonality to its limits.

The twelve-tone technique substitutes the melodic strand of a work by a
formulated succession of sounds (the series or the trope), whose interval
order engenders an atonal language. Bimodalism, in
contrast, not only rejects all forms of serial composition, but it also
indiscriminately uses any scalar degree to create melodies of a traditional
style.

To direct the musical flow to all scalar degrees (while ensuring that
no degree assumes greater prominence than another), one does not need to
nullify tonality, as the twelve-tone technique has done.

Bimodalism can direct the musical flow to all scalar degrees without
nullifying tonality, by reducing tonality to its harmonic quintessence:
the bimodal chord.

By harmonizing each degree of the chromatic scale with the bimodal
chord, each degree assumes equal prominence. From this ground, homogeneity
(a quality that is proper of tonal harmony) becomes a common attribute of
all chordal relationships within the scale.

In other words, all chordal relationships become closer; but these
relationships sound even closer, when they keep notes in common or when
they are formed by chords whose roots are separated by consonant intervals
(such as perfect fourths or fifths). In both cases, such relationships are
consequently easier for the ear to identify.

In fact, Bimodalism creates a sort of harmonically equalized
unitonality, synthesizing modal variety in the bimodal chord, where
chordal relationships built only with bimodal chords show just as much
homogeneity as those of the classical tonality, and where the trace of all
elementary chordal progressions from the classical tonality are easy to
follow by ear, although they are now made strictly of bimodal chords.

Intending to put an end to the chaos of atonality that late
post-Romanticism brought about, the Second Vienna School systematized
atonality in an aesthetic dogma, whose restrictive rules are comparable to
those of early polyphony in history.

Thus, by inventing a system of musical composition, the twelve-tone
technique created the serial form in music. A form that shines like a lone
star, once tonality, melody and harmony were extinguished in the musical
sky.

Soon thereafter, by applying the serial form to all compositional
elements in music, the Second Vienna School brought this to its
apotheosis: Form, so proclaimed by the School, is the most important
matter in music!

As for serial form, however, one may argue that its perception is more
visual than aural: When one reads a serial music score, the perception of its
form is clear to the eye; but when one then listens to the same score, the ear
no longer perceives its form as did the eye.

On the contrary, the ear actually loses all trace of form, perceiving
only a disordered mass of sounds in perpetual collision.

Therefore, is serial music for the eye or for the ear? More realistically, can
one say that what is appealing on paper is equally appealing when played?
I think not.

The horizontal path of sounds deliberately chained to align them
perpendicularly with other parallel sounds either produces a concordant or
discordant effect. If the result is concordant, as you would have in tonal
counterpoint, the form from the placement of these sounds stands out
easily to the ear; but, if the result is discordant, as you would have in
serial atonalism, the form (serial or tropal) is overshadowed and the ear
cannot perceive it; the trace of form is lost, in other words. (Atonality
rendered unintelligible the only language we all understood.)

Hence, the elements useful in an aesthetic judgment of mere graphic forms
play no role in music by themselves. The ear can only perceive
musical form acoustically in the more or less near presence of tonality: The greater the
tonal presence, the greater the perception of form.

Herein lies the paradoxical dilemma of atonalism, where the musical
form—the prime compositional element to be judged in this kind of music—is
actually not catchy to the ear. This paradox may have been signaling over
the decades that form, in music, is inherent to tonality.

Therefore, it is unwise to separate form from tonality as serial and
polytonal music have done, as there is no way to discern form, if one does
not present it to the ear within a certain atmosphere of tonality.

Perhaps, in lacking tonal sensation, no kind of atonality has ever
stimulated worldwide audiences over time, although this style of music has
been represented by some of the most conspicuous personalities of
twentieth-century music.

Bimodalism, contrary to all mathematical formulation or aleatoric practice
in
music, adopts and develops thematic form, as only this form can bring out
the musical wealth that tonality bequeathed us.

Therefore, Bimodalism has no place in serial or aleatoric formulation
of form. (Art is emotion: A work of art is merely a dexterous formulation,
if it does not pour out from the fonts of the subconscious, where emotion
is transmuted into metaphorical language.)

A musical style such as minimalism, however, which marks an abrupt return
to thematic form within tonality, may employ bimodal harmony in its
monothematic expositions ad infinitum.

In fact, Bimodalism and minimalism have two aesthetic principles in
common: Both represent a reaction against atonality, and both return to the
tonal thematic form.

But in returning to tonality and thematic form, Bimodalism and minimalism
differ greatly in their procedures: Minimalism returns to tonality without
reforming it, whereas Bimodalism revives tonality by radically reforming its
harmonic organization.

Moreover, as minimalism returns to thematic form without developing it,
Bimodalism returns to all the forms of thematic development, rejuvenating
them with a hitherto unheard harmonic touch. (Perhaps, Bimodalism is a
dimension and ethos that tonality reserved for its very own survival).

In short, while the twelve-tone technique and polytonality are schools of
modern counterpoint (aimed at developing polyphonic textures that nullify
tonality), Bimodalism, in contrast, is a harmonic system whose achievement
is to bring tertian harmony to its ultimate consequence: the modal unity of
the perfect chord (the unique harmonic element that Bimodalism uses
throughout the chromatic scale).

There have been sparse instances of bimodal chords adrift on the musical
ocean of the twentieth century, either by modern contrapuntal incidence or for a
sought-after color effect.

Notwithstanding, Pietro Raimondi’s Esempio No.4, from
Due Fughe In Una
(1849) for two mixed choruses and organ, cannot be considered a case of
early Bimodalism in history, as the composer consciously eludes the
simultaneity of both thirds on the modal degrees of the work in question.

As Raimondi admitted, "Molto difficile mi è riuscito questo esempio, per
causa delle terze ora maggiori, ed ora minori, secondo le circostanze, onde
non guastare il canto." [This example has been quite challenging
for me, first in handling the major third, then the minor, such that the
singing would not be impaired in any case.]

His procedure was ingenious: As one chorus sings in D major, the other
sings in D minor, neither chorus coinciding harmonically in the modal thirds
throughout the piece.

Esempio No.4 therefore does not consist of the simultaneity of the two
modes, chord by chord, which is precisely what Bimodalism is about.

Moreover, we may not allude to the first part of Stravinsky’s cantata,
Le roi et les étoiles (1911), as a case of contemporary Bimodalism,
as the principles of harmonic analysis classify the chord of the major and
minor thirds that characterize its harmony, as a simple dominant seventh
chord with an augmented ninth added: C-E-G-Bb-D# or Eb (9+).

To assume that this latter augmented ninth interval is the minor third
of the chord in question is theoretically incorrect, because this assumption
ignores the order and variable qualities of the chordal degrees in the
tertian harmony.

Therefore, chords such as those in Stravinsky’s cantata, which are
integrated by other voices beyond the perfect triad, are not purely bimodal:
In this case, the presence of a minor seventh changes the denomination of
the bimodal triad and its proper identity of sound (the bimodal ethos). (It
is worth noting that, as long ago as young Gershwin's day, this augmented
ninth chord has found a place in the harmonic palette of Jazz.)

Stravinsky did, notwithstanding, use purely bimodal chords on occasion,
but this was mostly in its embryonic phase. One can therefore find specimens
of these chords scattershot throughout the body of his work.

We must not assume, however, that such a deliberate use of these chords
within isolated segments from a few of Stravinsky's many works implied an
underlying purpose in developing a new school of harmony based on Bimodalism.

Far from this, the ongoing change in style that Stravinsky experimented
with throughout his career—be it polytonalism, pandiatonicism,
neoclassicism, or even
Webernian serialism (to which he was lately inducted)—clearly demonstrates
that these meant nothing more than a mere compositional resource at the
service of his aesthetic thinking.

As far as I know, a prototypical work, deliberately written
to represent
Bimodalism, has never been published or
mentioned in the accredited literature of music.

But even if such a paradigm were to exist as an isolated
laboratory experiment, it would in no way cast a shadow over the value and originality of this invention: to create
a harmonic system that gives music a new dimension and ethos embodied in
Bimodalism.

If some bimodal work did exist previously, rather we ought to agree with
Goethe that, once again, "future events cast their shadows in advance."

In light of this sense of forecasting, we must recall that

four centuries ago, Luca Marenzio (1553-1599) and Carlo Gesualdo
(1560-1613) independently wrote madrigals that could have been written by
a Richard Strauss;

as for
Hans Neusiedler's (1508-1563) work, Der Juden Tanz (The Jew’s Dance),
there are numerous records in the seventeenth century where the police of
Prague leveled charges against Jewish musicians for improperly playing
"scales, modes, and functional harmony" in this dance, which prompts us to
file this work among the earliest cases of modern bitonality, and not as a
case of scordatura;

both Chopin and Liszt, each intending to expand tonality, wrote
ostensible passages in a frank atonality;

Giovanni Battista Vitali (1644-1692) fully constructed the cyclical
form of the sonata, two centuries before César Franck accomplished it in
his Sonata in A for piano and violin;

it is Ernest Fanelli (1860-1919), not Debussy, who we should
acknowledge as the father of musical Impressionism, upon hearing his
Tableaux Symphoniques (1882) recently recorded on compact disc;

the unfairly forgotten Pietro Raimondi (1786-1853) deliberately and
systematically wrote an ingenious collection of fugues in four and six
simultaneous tonalities, apart from his Three Oratorios In One,
juxtaposing contrary tempos and meters, long before Milhaud, Prokofiev, Bartók
(or even Ives) began to experiment with polytonality and Stravinsky,
Carter, and Blacher, with polymeter, metric modulation and variable
meters, respectively;

the virtuoso pianist Charles Kunkel (1840-1923) used a tone cluster
effect in his work, Alpine Storm (1888), before Charles Ives used this
effect in 1911 in the second movement of his Concord Sonata, and before
Henry Cowell — its principal user — coined the term in 1915;

a Clavecin Oculaire, invented in 1734 by Louis-Bertrand Castell
(1688-1757), preceded by almost two centuries the synaesthetic inventions
of sound and color that Scriabin exhibited in his Prometheus (1910);

microtonality, since its extinction in Greek antiquity, reemerged
systematized by the astronomer Christiaan Huygens (1629-1695) in his
Tricesimorprimal Temperament, many times before Jacques Halévy practiced
microtonality in his cantata, Prométhee Enchaîné (1847), and before
Richard Stein (1882-1942), Alois Hába (1893-1973), and Julián Carrillo
(1875-1965) with his Sonido 13, made their first experiments
fractionalizing the octave into several microtones of different values;

as history now sheds light, it was Charles Ives (1874-1954), who first
used a twelve-tone row, before J. M. Hauer, Schoenberg and Jefim Golyscheff
were to divulge their own serial techniques amid a paternity contest
claiming credit for the idea itself;

in 1914, Erik Satie instructed that sheets of paper be
inserted between piano strings in Le piège de Méduse, and Rued Langgaard
(1893-1952) instructed that a glissando be played on the piano strings in
Sfaerernes musik (1918), before John Cage (following Cowell’s experiments,
respectively) could have embodied all these ideas in his Prepared Piano or
Klaviergamelan (1940), whose industrialization and universality were owing
to the inventions by its performer and promoter, Richard Bunger (q.v.: Bungerack, Pianotation, and so forth);

in his work, Das Eisige Lied (The Icy Song), and in his opera, Cyrano
de Bergerac, the Dadaist Jefim Golyscheff (1897-1970) employed a noisy
collection of domestic objects, three decades before Pierre Schaeffer
(1910-1995) would formulate his theory of musique concrète in 1948;

Ravel's Boléro (1928) should be considered the true forerunner of
minimalism, a work that features all the components of this style;

12 years before George Crumb premiered his work, Ancient Voices of
Children (1970), I created musical vocal effects by sympathetic resonance
within a piano, in my incidental music composed for Jean Anouilh's drama,
Roméo et Jeanette, performed at the Fine Arts Palace of Havana;

and that Mozart — two centuries after Der Juden Tanz had
materialized — not only added to the dossier on bitonality as initiated in
that dance with his own Ein Musikalischer Spaß,
but once again, amusing himself, threw the dice to vary
the numerical order of a group of written measures, long before John Cage,
Karlheinz Stockhausen, Pierre Boulez, and many other composers were to
write aleatoric music in our day.

The challenging character of these historic events, however, should not
alter our wise evaluation of the matter at hand: In art, the paternity of an
aesthetic idea is not consequently attributed to who, by hazard or by
genius, originates the essence of the idea, but to who — regardless of
claims to origination — develops the idea to its consecration.

Indeed, ever since I wrote several works employing this harmonic element
as an aesthetic principle of musical composition, Bimodalism has finally
developed into and
become a recognizable system with its own identity, as a new world-class school
of contemporary harmony.

Click above for my digital guitar recording of The Sleepless Street.
This is a work for solo classical guitar written entirely in
bimodal harmony. I composed it to pay homage in dance form to the many jazz
clubs that existed along New York's West 52nd Street from the 1930s to the
1950s.

One of my master class composition students, Peter Corey, was also an
accomplished classical guitarist, and in 1984 he premiered this work at
Merkin Concert Hall. Allen Hughes of the New York Times, who reviewed it
back then, felt it was “a pretty little piece with mildly piquant dissonance
deriving from bimodal treatment.”

I wish to point out that The Sleepless Street is only one of several
compositions I've written in bimodal harmony. I chose it as an example for
this web page because its homophonic simplicity unmistakably highlights the
harmonic novelty of Bimodalism. As time permits, I intend to add other
examples consisting of chamber and orchestral works to showcase Bimodalism
with a greater complement of compositions.

Melody is an outline; harmony is a mass; rhythm is a motion...Music is the outline of a mass in motion.